To find the kinetic energy of the orca, we can utilize the kinetic energy formula:
[tex]\[ E_k = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the orca,
- [tex]\( v \)[/tex] is the speed of the orca.
Let's plug in the values provided:
- [tex]\( m = 3250 \, \text{kg} \)[/tex]
- [tex]\( v = 15 \, \text{m/s} \)[/tex]
Next, we will calculate the kinetic energy step by step.
1. First, square the speed [tex]\( v \)[/tex]:
[tex]\[ v^2 = 15^2 = 225 \, (\text{m}^2/\text{s}^2) \][/tex]
2. Then, multiply the mass [tex]\( m \)[/tex] by this squared speed [tex]\( v^2 \)[/tex]:
[tex]\[ m \times v^2 = 3250 \times 225 = 731250 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
3. Finally, divide the result by 2 to get the kinetic energy:
[tex]\[ E_k = \frac{731250}{2} = 365625 \, \text{J} \][/tex]
Therefore, the kinetic energy of the orca is:
[tex]\[ E_k = 365625 \, \text{J} \][/tex]
